Learn Portuguese (Portugal): Ele pôde ganhar o jogo e agora acha-se muito. - He was able to win the game and now he thinks highly of himself.

The verb achar normally means to find, think, or believe. However, when used as a reflexive verb (achar-se), it takes on a new meaning. It becomes an informal expression meaning to think highly of oneself, to be arrogant, or to be full of oneself.

Why does the sentence use pôde instead of podia?

Pôde is the simple past (pretérito perfeito), which shows that he had the ability to win on one specific occasion and that he actually succeeded in doing it. If the sentence used podia (the past imperfect), it would just describe his general ability, meaning he had the potential to win, but not necessarily that he actually did.

Why is the pronoun placed after the verb in acha-se?

In European Portuguese, the default position for a pronoun in an affirmative main clause is after the verb. While certain adverbs can pull the pronoun to the front, in coordinate clauses joined by e like this one, it is standard to keep the pronoun attached to the end of the verb with a hyphen.

Does acha-se always need to be followed by muito?

No, the verb achar-se stands on its own to mean being full of oneself. Adding muito simply acts as an intensifier. You will also commonly hear variations like ele acha-se o maior (he thinks he is the greatest).